360x-240/3x=100

Solution for 360x-240/3x=100 equation:

360x-240/3x=100

We move all terms to the left:

360x-240/3x-(100)=0


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R


We multiply all the terms by the denominator


360x*3x-100*3x-240=0

Wy multiply elements

1080x^2-300x-240=0

a = 1080; b = -300; c = -240;
Δ = b2-4ac
Δ = -3002-4·1080·(-240)
Δ = 1126800
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{1126800}=\sqrt{3600*313}=\sqrt{3600}*\sqrt{313}=60\sqrt{313}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-300)-60\sqrt{313}}{2*1080}=\frac{300-60\sqrt{313}}{2160}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-300)+60\sqrt{313}}{2*1080}=\frac{300+60\sqrt{313}}{2160}
$